"Nuoc mam" is much less ambiguous than using "fish sauce", so using the translation seems like a lot of precision is lost. Plus, "nuoc mam" is the standard romanization of "nước mắm", which is admittedly difficult to type on QWERTY keyboards + en-* locales.
If you're talking about "nước chấm", as far as I know that is a class of dipping sauces that include things besides just "nước mắm"[0].
These will be things from SMCP's style guide and will be shared by many other publications, because it's the way most of us treat other languages. There's a similar treatement of name order. I think the style shows disregard for the languages and cultures, so I don't like it.
Diacritics are pretty rare in English publications for the most part: most drop diacritics even off of the English words that technically should have them: cliché, crêpe, façade, piñata, protégé, résumé, risqué... Even the New Yorker, with its famously persnickety style guide, drops the tone diacritics from Vietnamese dish names: https://www.newyorker.com/magazine/2019/05/27/van-das-tour-o...
Outside of this, I think the point about "nuoc mam" being the standard (complete) romanization still stands: it is common enough that some common English dictionaries have added it (eg https://www.merriam-webster.com/dictionary/nuoc%20mam and https://www.collinsdictionary.com/dictionary/english/nuoc-ma...). This is quite a common occurrence in languages which use the Latin alphabet + additional letters: most speakers of German are used to seeing "ß" become "ss" in English publications. I can see why you interpret this as a disregard for other languages, but people are more likely to try to say these words if they think the word is easily pronounceable. And using the word makes the foods, places, names, etc of other cultures more likely to be shared and become a part of the common parlance; I'd go so far as to say that having an anglicized form of a name means that it is much more likely to become a common thing in the Anglophone world, which breeds greater appreciation of other cultures.
This is a plausible sounding line of thought but English-language sources are rarely consistent about it. In particular, Western European languages, especially French, often get to keep their accents even though they are meaningless to English speakers.
Compare, for instance, how many places will write "Côte de bœuf" but "nuoc mam". German, Spanish, Portugese, and Swedish are other languages where I often see "weird letters" and diacritics left in, even in English-language publications that don't do the same favors for other languages.
That said, it is possible that SCMP is consistent about this so I don't want to call them out as hypocritical without checking.
Some words have been imported and adapted into English in the past, but I doubt that nước mắm is one of them.
I‘d also say that news outlets should be held to a higher standard than “conversational language.”
But of course, this is all BS. Languages constantly borrow new words. 20 years ago, nobody knew what "pho" or "banh mi" were, but now we all do. We know what it means so much that we leave off the diacritics entirely and nobody is confused. Those diacritics cannot be represented within the framework of English. They're components of a completely different language.
Is it unreasonable that English speakers today will borrow the word "nuoc mam" and use it in normal English conversation? I've already been seeing it on recipe sites for a couple years now. It's about as English as kimchi and ramen. Nobody ever has or ever will look up the hangul or katakana to write about those in an English article, despite them being easy to remember. "nước mắm" is a foreign word written in its language. "Nuoc mam" is the thoroughly transliterated, romanized equivalent. This phenomenon exists in every language on earth that has ever come in contact with another culture. There isn't a higher standard to hold the author to--they're writing how humans do.
It should also be noted that most Vietnamese people don't really care about texting without diacritics. Most text messages are written without diacritics in order to minimize the payload size. It's just about perception when you see foreign western dishes with their diacritics like crème brûlée but see foreign eastern dishes without theirs.
English has plenty of French loanwords, and for the most part, we drop the accent marks. Not because of disrespect for the French, but because they're simply extraneous in our language. Nobody is looking up the word every single time they write it. They've become accepted as having a distinct meaning within of our language, just like nuoc mam.
Let people write the way they want, no matter who they are, as long as point gets accross.